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How many ways can 4 men and 4 women sit in a row of 8 seats such that no two men sit together?

Assume that all people are distinguishable. So if Fred and Ted switch places, it's a different formation.

 Jun 16, 2020
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I believe that they can be seated as:

 

M-F-M-F-M-F-M-F

M-F-M-F-M-F-F-M

M-F-M-F-F-M-F-M

M-F-F-M-F-M-F-M

F-M-F-M-F-M-F-M

 

In each case there will be 4 x 4 x 3 x 3 x 2 x 1 x 1 = 576 was.

 

5 x 576 = 2880 ways

 Jun 16, 2020

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